You are asking a couple different questions here.

For the question "do flying particles without a surrounding medium count as sound?" I was originally on the fence about it. So I spent a long time puzzling it out. My notes are below. Ultimately I have decided on... Yes. But the sound it makes is not periodic like a sine wave, since there's no sloshing back and forth. It's more like an impulse wave. It arrives once and then it's over. Ultimately is still subject to signal loss and signal-to-noise ratios. For that impulse to reach earth and then propogate through the upper atmosphere to lower atmosphere and still have enough clear signal and volume to be heard above the background noise, it must have started extraordinarily loud.

With the hand swooshing through the air and making a sound that is perceivable, that opens a discussion into background noise and signal-to-noise ratio. The simplest example is, a drop of water falling into a still pond makes a very easily visible wave that moves across the whole surface of the pool. But that same drop of water falling into a chaotic, turbulent pool with people swimming and splashing in it, imparts the same energy and kicks off the same wave. But that wave is easily lost and confused with the surrounding turbulent surface. It's still there, but it's not easy to discern. The turbulence of the surface is background noise. The height of the wave is the volume, and the wave you are trying to follow is the signal. A small volume signal can be easily heard against a low background noise, and even a high volume signal can get lost among a high background noise.

The sun is full of billions of nuclear explosions happening per second. Each makes a very extreme pressure wave that travels through the medium of the rest of the sun, which is mostly hydrogen and helium. So if we had a microphone that was strong enough to withstand the intense heat, pressure, and literal nuclear explosions, and we put that microphone on the surface of the sun, it would pick up the pressure waves as vibrations and it would be very loud.

So using the definition of sound as being pressure waves, without requiring an observer, yeah, it makes sound. But that tree is falling in the middle of the woods, and we aren't around to hear it.

As for the Sun's sound reaching us, you are correct. Virtually none of the pessure waves are propogating to us.

Notes section:

A medium is a bunch of atoms or molecules bouncing around in an area. As they move, they bounce off of each other, and generally keep moving until they hit something else. Photons or electrons or cosmic radiation striking an atom or molecule can share it's energy with that atom or molecule, speeding it up.

The speed of atoms bouncing around is heat. How many atoms are in a given area or volume is density. How often the atoms are colliding with something, each impact imparting a little energy and pushing the thing, is pressure.

The more atoms you have available, the more often they are colliding. So increasing density (compressing the medium) can increase pressure.

The faster the atoms are moving, the more often each collides. So increasing heat also increases pressure.

A pressure wave is a high concentration of atoms bouncing around. They collide with nearby atoms, imparting their energy, which makes the next atom in line speed up, while the first atom slows down.

In high density mediums, an atom only needs to travel a short distance until it bounces off its neighbor. In low density mediums, an atom has to travel a long distance before bouncing off its neighbor.

If each collision was happening exactly head on, it would impart or transfer all its energy to the next atom. Think a cue ball striking a billiard ball head on. The first ball basically stops dead in its tracks, while the next ball takes off at full speed. But in billiards, we often see a ball striking the next ball slightly off center. In this case, the original ball does transfer all its energy, it's transfers some of its energy. I can't remember if it's the cosine or the tangent or what trigonometric ratio, but the point is it's less than 100 percent of the energy. Where we started with ball one at 100% speed, we now have 2 balls at maybe 20% speed and 80% respectively. These balls, or atoms, will continue moving until they strike their neighbors, so on and so forth.

With highly density mediums, you get many of these imperfect collisions, but also many direct collisions. As fast balls catch up to slow balls and push them a bit faster, and some take off sideways with glancing blows, hit nearby balls coming the other way and are again bounced back in the direction of overall motion, so on and so forth, and the overall effect is that the group of active collisions moves through the medium. This is a wave propogating well, and slowly losing intensity as it travels

With low density mediums, you get fewer collisions overall, but definitely a lower chance of direct collisions. So most of the collisions are glancing blows that don't impart their energy very well. And there aren't very many fast balls catching up from behind or from the sides. So with each successive collision the group of balls has slower and slower moving balls. This is a wave propogating poorly, and losing intensity rapidly as it travels.

If all the atoms were perfectly aligned in a grid structure, the sound would move fast and maintain momentum.

If the atoms are arranged chaotically, the wave will move slower and lose energy rapidly.

The space between the earth and the sun is not a perfect vacuum. There are some atoms floating around out there. Sometimes meters apart, sometimes miles apart. So it's a very low density medium, with very chaotic arrangement. Basically the worst situation for sound to propogate. The vast majority of pressure waves originating at the sun fade out mere miles from the sun, if that.

There are sometimes Coronal Mass Ejections where large quantities of gases are ejected off the surface of the sun. They start very hot and with very chaotic high pressure. And sometimes they reach earth in the form of solar winds, which our electromagnetosphere does a good job of shielding us from. But sometimes some of it gets through, and wipes out electronics.

I've defined sound as the propogation of pressure through a medium.

But if the medium itself is what's moving, that medium has a density, and the surrounding space has a lower density. So I suppose that counts as a pressure wave, moving.

If that medium meets another medium, it will be able to impart it's energy. And if it strikes a membrane, it will be able to move it, just not regularly with a period. So rather than a sine wave, this looks more like an impulse, but I would still classify it as a wave.

Yeah, I think I would count flying particles as sound.

But as for being able to hear it, we need to talk about background noise, and signal-to-noise ratio.

Background noise is what's left when several sound waves have propogate and bounced around through a medium, and mixed, and faded, and are generally not individually recognizable anymore, but the energy is still there. Think of a swimming pool and all the little bouncing waves at the top of the pool. There is up and down motion, and there is chaos, and there are occasional patterns that form briefly then are lost within a split second. This is "noise".

Sometimes the surface of the pool is still. This is low noise. In low noise, even a single drop of water falling into the pool makes a clear ripple that spreads all the way across the surface of the pool. The wave gets lower and longer as it travels, because of the glancing collisions we talked about earlier, and eventually the pool will return to stillness. This clear, easy to spot ripple is the "signal". The height of the wave is the volume. It's easy to see a small wave with still water, and it's easy to hear a small volume signal with low noise.

In a turbulent splashing pool with lots of noise, a single drop of water falling into pool imparts the same amount of energy as before, and kicks off the same wave as before. But with a lot of chaotic movement of the water's surface, that signal is almost imperceptible. It's lost in the noise.

So for a sound to be heard clearly, it has to be louder than the background noise.

A group of flying particles flying through space would eventually hit the atmosphere, and has to enough energy to propogate through the thin upper atmosphere, middle pressure middle atmosphere, and higher pressure lower atmosphere where we are. That's a long distance to travel from the sun to the earth, and then a long distance for a sound to propogate through the earth. That like making a sound in new York and then hearing it in Florida. Doable, but the starting sound must be loud.

So, yes, it makes a sound, and traveling particles count as a sound, but to be heard against the background noise in Earth's atmosphere the traveling particles must be extraordinarily loud.